Ramification Index
المؤلف:
Jones, G. A. and Singerman, D.
المصدر:
Complex Functions Cambridge, England: Cambridge University Press,
الجزء والصفحة:
p. 196
28-7-2021
1811
Ramification Index
For a point 
, with 
, the ramification index of 
at 
is a positive integer 
such that there is some open neighborhood 
of 
so that 
has only one preimage in 
, i.e., ![f^(-1)(x) intersection U=<span style=]()
{y}" src="https://mathworld.wolfram.com/images/equations/RamificationIndex/Inline10.gif" style="height:17px; width:102px" />, and for all other points 
, 
. In other words, the map from 
to 
is 
to 1 except at 
. At all but finitely many points of 
, we have 
. Note that for any point 
we have 
. Sometimes the ramification index of 
at 
is called the valency of 
.
REFERENCES:
Jones, G. A. and Singerman, D. Complex Functions Cambridge, England: Cambridge University Press, p. 196, 1987.
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